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x, y, z, and w are integers. The expression x-y-z is even and the
Expression y-z-w is odd. If x is even what must be true?
Expression y-z-w is odd. If x is even what must be true?
- a)y-z must be odd.
- b)w must be even.
- c)w must be odd.
- d)z must be even.
- e)Z must be odd
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
x, y, z, and w are integers. The expression x-y-z is even and theExpre...
The best answer is C.
The first expression is even and the second is odd, the differences between the two expressions is x instead of w. (remember, there is no difference in odd/even numbers if the number is positive or negative so y-z is like z-y). Therefore if x is even w must be odd.
Most Upvoted Answer
x, y, z, and w are integers. The expression x-y-z is even and theExpre...
Given information:
- x, y, z, and w are integers.
- x-y-z is even.
- y-z-w is odd.
- x is even.
To find:
What must be true?
Solution:
1. Analyzing x-y-z is even:
- We are given that x-y-z is even.
- We know that the difference of two even numbers is always even.
- Since x is even, y and z can be either even or odd.
2. Analyzing y-z-w is odd:
- We are given that y-z-w is odd.
- We know that the difference of an odd number and an even number is always odd.
- Since y-z-w is odd, y and z cannot both be even.
- If y and z are both odd, then w must be even to make y-z-w odd.
- If y is even and z is odd, then w can be either even or odd to make y-z-w odd.
3. Analyzing possible scenarios:
Now, let's analyze the possible scenarios based on the given information:
Scenario 1:
- y and z are both odd.
- In this case, w must be even to make y-z-w odd.
- This scenario satisfies all the given conditions.
Scenario 2:
- y is even and z is odd.
- In this case, w can be either even or odd to make y-z-w odd.
- This scenario satisfies all the given conditions.
4. Conclusion:
Based on our analysis, we can conclude that if x is even, then w must be odd. Therefore, the correct answer is option C: w must be odd.
- x, y, z, and w are integers.
- x-y-z is even.
- y-z-w is odd.
- x is even.
To find:
What must be true?
Solution:
1. Analyzing x-y-z is even:
- We are given that x-y-z is even.
- We know that the difference of two even numbers is always even.
- Since x is even, y and z can be either even or odd.
2. Analyzing y-z-w is odd:
- We are given that y-z-w is odd.
- We know that the difference of an odd number and an even number is always odd.
- Since y-z-w is odd, y and z cannot both be even.
- If y and z are both odd, then w must be even to make y-z-w odd.
- If y is even and z is odd, then w can be either even or odd to make y-z-w odd.
3. Analyzing possible scenarios:
Now, let's analyze the possible scenarios based on the given information:
Scenario 1:
- y and z are both odd.
- In this case, w must be even to make y-z-w odd.
- This scenario satisfies all the given conditions.
Scenario 2:
- y is even and z is odd.
- In this case, w can be either even or odd to make y-z-w odd.
- This scenario satisfies all the given conditions.
4. Conclusion:
Based on our analysis, we can conclude that if x is even, then w must be odd. Therefore, the correct answer is option C: w must be odd.
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x, y, z, and w are integers. The expression x-y-z is even and theExpression y-z-w is odd. If x is even what must be true?a)y-z must be odd.b)w must be even.c)w must be odd.d)z must be even.e)Z must be oddCorrect answer is option 'C'. Can you explain this answer?
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